Real-Time Quantum Dynamics of Electron–Phonon Systems (eBook)

Supervisors’ Foreword 7
Abstract 9
Acknowledgements 10
Contents 11
Abbreviations 14
1 Introduction 16
References 21
2 Physical Motivation 23
2.1 Radiation Damage 23
2.1.1 Radiation Damage in Metals 25
2.1.2 Radiation Damage in Biological Systems 27
2.2 Ultrashort Laser Heating of Metals 30
References 34
3 Simulating Electrons and Phonons: Effective Temperature Methods 37
3.1 An Effective Temperature Model for Radiation Cascades 38
3.2 The Two-Temperature Model (2TM) 39
3.3 The 2TM in MD Simulations 42
3.3.1 Augmented MD Models, the Langevin Equation 44
3.3.2 Inhomogeneous Models 46
References 50
4 Simulating Electrons and Phonons: Atomistic Methods 52
4.1 A Simple Classical Model and the Born-Oppenheimer Approximation 53
4.2 Ehrenfest Dynamics 55
4.2.1 A One-Sided Electron-Atom Heat Exchange 58
4.3 Correlated Electron-Ion Dynamics (CEID) 60
4.3.1 CEID Simulations 62
4.4 The Bonca-Trugman Method 66
References 68
5 The ECEID Method 70
5.1 The Model 70
5.2 An Exact Form of ?(t) and ?(t) 72
5.3 The Approximations 75
5.4 ECEID's Equations of Motion 76
5.5 From Many-Electron to One-Electron Equations of Motion 78
5.6 Total Energy Conservation 79
5.7 Open Boundaries in ECEID 80
5.8 Implementing ECEID in a Computer Simulation 81
5.8.1 Code Breakdown 82
References 83
6 ECEID Validation 84
6.1 Comparison with an Exact Simulation 84
6.1.1 An Exact Limit on a 2-Level System with 1 Oscillator 86
6.1.2 Extension to a 3/Many-Level System with 2 Oscillators 88
6.2 Mimicking an Extended System and Energy Conservation 91
6.3 Validating the Open Boundaries 92
6.4 Joule Heating 93
6.4.1 A Microscopic Ohm's Law 96
6.4.2 Onsite Disorder 99
6.5 Code Performance 101
References 105
7 Thermalization with ECEID 106
7.1 The System 108
7.2 An Entropic Definition of Temperature 108
7.3 Comparison with Ehrenfest Dynamics 109
7.4 Results 110
7.4.1 Thermalization 110
7.4.2 Population Inversion 110
7.4.3 Kinetic Model 111
References 114
8 Inelastic Electron Injection in Water 117
8.1 Water Molecule 118
8.1.1 A Simple Water Model 118
8.1.2 Embedding Setup 120
8.1.3 Elastic Transmission 121
8.1.4 ECEID Comparison with Elastic Averages 123
8.1.5 The Landauer and the High Mass Limit 127
8.1.6 Current Assisted Phonon Heating 130
8.2 Water Chain 132
8.2.1 The Model 132
8.2.2 Simulation Details 135
8.2.3 Electron-Pulse Injection 136
8.2.4 Electron-Gun Injection 138
8.2.5 Eigenstate Lifetime and Band Edge Trapping 140
References 142
9 A New Development: ECEID xp 144
9.1 A Canonical Transformation 144
9.2 Exact Dynamics 146
9.3 The Approximations and ECEID xp 148
9.4 An Ehrenfest-Like Condition for x?(t) 150
9.5 A Test Case 152
9.6 Code Performance 156
9.7 Final Remarks 156
References 158
10 Conclusions and Perspectives 159
References 162
A Electronic Operators in ECEID: From Many-Body to Single Body 163
A.1 Tracing Over the Electrons 163
A.2 Tracing the ECEID Many-Body EOM 164
Appendix B Open Boundaries in ECEID 167
B.1 General Formalism 167
B.2 Elastic Transmission 169
B.3 Including the OB in ECEID 170
B.4 Imposing a Constant Bias in the Leads 171
B.5 Other Injection Setups 173
Appendix C An Alternative Water Chain 174
C.1 Simulation Details 174
C.2 Electron-Pulse Injection 177
C.3 Electron-Gun Injection 179
C.4 Eigenstate Lifetime and Bandedge Trapping 179
Appendix D Beyond the Double (De)excitation Approximation 182
References 184